Least Common Multiple (LCM) of 19 and 149
The least common multiple (LCM) of 19 and 149 is 2831.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 19 and 149?
First, calculate the GCD of 19 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 149 = 0 remainder 19 |
| 2 | 149 ÷ 19 = 7 remainder 16 |
| 3 | 19 ÷ 16 = 1 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 46 | 690 |
| 84 and 165 | 4620 |
| 120 and 30 | 120 |
| 49 and 42 | 294 |
| 166 and 143 | 23738 |